Symmetric wrinkling - TU Delft OCW · 2016-02-02 · the failure mode switches from antisymmetric...

Symmetric wrinkling

• the derivation so far assumed that the core is

sufficiently thick so that zc≤tc/2

x

z

ℓ

zc

zcA

• if (5.5.3.2.13) gives zc>tc/2, then

2

cc

tz (5.5.3.2.13a)

• substituting in (5.5.3.2.11) 4/1

3

4/124

cf

c

ftt

E

E (5.5.3.2.14a)

Symmetric wrinkling

• and substituting for zc and ℓ in (5.5.3.2.10),

6816.0

3

c

xz

c

fcf

xwr

tG

t

tEEN (5.5.3.2.15a)

• to find the condition for the full-depth of the core

being “active” (zc=tc/2) use eq. (5.5.3.2.13):

3/1

2817.1

xz

cf

fcG

EEtt (5.5.3.2.16)

• if (5.5.3.2.16) is valid, then zc=tc/2 and eqs (5.5.3.2.14a)

and (5.5.3.2.15a) are valid; otherwise, (5.5.3.2.13)-

(5.5.3.2.15) are valid

Anti-symmetric wrinkling• in an analogous fashion but with different starting

assumption for w(x,z), the following expressions are

obtained for anti-symmetric wrinkling(1,2)

x

z

(5.5.3.2.17)

(1) Hoff, N.J.,Mautner, S.E., “The Buckling of Sandwich-Type Panels”, J Aeronautical Sciences, July 1945, pp 285-

297

(2) Vadakke, V., and Carlsson, L.A., “Experimental Investigation of Compression Failure Mechanisms of Composite

Faced Foam Core Sandwich Specimens”, J. Sandwich Structures & Materials, 6, 2004, pp. 327-342

3/1

2

6/12

3/1

2

3

15.2

351.0

xz

cf

fc

xzc

f

f

cxz

xzcffxwr

G

EEtz

GE

Et

tGGEEtN

3/1

23

xz

cf

fcG

EEttfor

Anti-symmetric wrinkling (cont’d)

x

z

4/1

2/3

67.1

378.059.0

fc

cf

f

cxz

c

cf

fxwr

tE

tEt

tGt

EEtN

3/1

3

xz

cf

fcG

EEttfor (5.5.3.2.17a)

Wrinkling – comparisons with FE

predictions

• the previous analysis for wrinkling assumed perfectly

flat facesheets; in practice, the facesheets are wavy

unless they are pre-cured and then bonded on the

facesheet; for this reason, test results with flat facesheets

are hard to come by and of little practical interest since

facesheets are, typically, co-cured with the core as part

of the same cure cycle.

• therefore, the easiest comparison is with a detailed FE

model

Wrinkling – Comparison with FE

predictions(1)

(1) Kassapoglou, C., Fantle, S.C., and Chou, J.C., “Wrinkling of Composite Sandwich

Structures Under Compression”, J Composites Technology and Research, 17, 1995, pp 308-

316.

• facesheet: (0/90)/(±45)2/(0/90) plain weave fabric with

thickness 0.76 mm

• core thickness= 25.4 mm (properties shown below)

Ec

(MPa)

Gxz

(MPa)

Nxwr/tf (MPa)

present

Nxwr/tf (MPa) FE

Δ% ℓ (mm)

present

ℓ (mm)

FE

Δ%

133 42 646 658 -1.8 11.3 11.4 -0.9

266 42 842 1033 -18.5 9.5 8.9 +6.7

133 84 808 821 -1.6 10.6 13.2 -19.7

Wrinkling – Some points• the discussion so far did not explicitly account for the

fact that the facesheet is composite; only the value of Ef

appropriately calculated would bring composites in the

picture

• some researchers have explicitly included composite

facesheets in the derivation; for example, for symmetric

wrinkling the wrinkling load expression is(1):

facesheet buckling load core (elastic found-

ation) contribution

Note the similarity with our “generic” eq. (5.5.3.2.10) and the fact that

the contribution from core shear is missing here!

(1) Pearce, T.R.A. and Webber, J.P.H., “Buckling of Sandwich Panels with Laminated Face

Plates”, Aeronautical Quarterly, 23, 1972, pp. 148-160

c

cf

fffxwrtm

aE

b

a

m

D

b

aDDmD

aN

22

24

2

222

6612

2

112

2 222

Wrinkling – Some Points

• to paraphrase P.A. Lagace, “there are as many wrinkling

equations as there are researchers in the field”; it is a

matter of preference which equations one uses and what

knockdown factors are appropriate to replace the

numerical coefficients

• a comparison of a variety of methods with test results

can be found in: Dobyns, A., “Correlation of Sandwich

Facesheet Wrinkling Test Results with Several Analysis

Methods”, 51st AHS Forum, Ft Worth, TX, May 9-11, 1995

• the main conclusion is that the presence of facesheet

waviness makes these methods unreliable (unless

properly “adjusted”)

Wrinkling – Effect of Waviness

portion of upper facesheet and core at 200X magnification

from: Kassapoglou, C., Fantle, S.C., and Chou, J.C., “Wrinkling of Composite Sandwich


316

Wrinkling – Effect of Waviness

• measured waviness from Kassapoglou et al

Wrinkling – Effect of waviness

• assuming waviness is periodic of known amplitude and

wavelength one can solve for the facesheet deflections

under compression(1)

(1) Kassapoglou, C., Fantle, S.C., and Chou, J.C., “Wrinkling of Composite Sandwich


316

C

max core tension

max facesheet bending

max adhesive tension

max core compression

max facesheet bendingmax core shear

max adhesive shear

Nxwr

Nxwr

Wrinkling – Using waviness to

predict failure

• measure amplitude and wavelength or determine

conservative values

• use bending modulus for the facesheet since the

facesheet is predominantly in bending

• apply equations for the different failure modes

– facesheet bending

– adhesive shear or tension

– core tension, compression or shear

Wrinkling – Using waviness to

predict failureFacesheet Core Predicted wr.

stress (MPa)

Test wr.

stress (MPa)Δ%

(±45)/(0/90) Nomex HRH10-1/8-3.0

295 313 -5.8

(±45)/(0/90)/ (±45) Nomex HRH10-1/8-3.0

264 297 -11.2

(±45)/(0/90)2/ (±45) Nomex HRH10-1/8-3.0

426 337 +26.4

(±45)/(0/90) Phenolic HFT3/16-3.0

344 350 -1.8

(±45)/(0/90)/ (±45) Phenolic HFT3/16-3.0

255 349 -26.9

(±45)/(0/90)2/ (±45) Phenolic HFT3/16-3.0

309 382 -19.0

(±45)/(0/90)/ (±45) Korex 1/8-3.0 246 365 -32.7

What does all this mean?

• methods not very reliable; require use of judgement, or

• use method of preference with appropriate knockdown factor

• recommended for design(1) (without need to check if full-

depth of core is effective unless tc<5mm):

(1) for 0.43 factor, see Bruhn, E.F., “Analysis and Design of Flight Vehicle Structures”, S.R.

Jacobs & Assoc, Indianapolis, IN, 1973, section C12.10.3;

for 0.33 factor, see Sullins, R.T., Smith, G.W., Spier, D.D, “Manual for Structural Stability

Analysis of Sandwich Plates and Shells”, NASA CR 1457, 1969, section 2

3/143.0 xzcffxwr GEEtN (5.5.3.2.18)

compare with 0.91 of eq. (5.5.3.2.15)

(symmetric wrinkling)

compare with 0.82 of eq. (5.5.3.2.17)

(5.5.3.2.19)

note core shear modulus is not

present

(anti-symmetric wrinkling)

c

f

f

cffxwr

t

t

E

EEtN 33.0

Implications of antisymmetric wrinkling equation

• as core thickness increases the wrinkling load decreases

• this is somewhat misleading; the equation is derived assuming perfectly

flat facesheets; the waviness present changes things

• antisymmetric wrinkling occurs for very thin cores; for larger tc values,

the failure mode switches from antisymmetric to symmetric wrinkling

• it is common to use only the symmetric wrinkling equation in design and

verify for shear crimping which is final outcome of antisymmetric wrinkling

0102030405060708090

100110120130140

0 5 10 15 20 25 30 35 40

c

f

f

cffxwr

t

t

E

EEtN 33.0

tc, mm

Nxwr

(N/mm)

Waviness favors symmetric wrinkling

Correction to wrinkling equations

• for more accurate representation of composite

facesheets, it is recommended to replace Ef in

the previous equations:

3

11)1(12

f

fyxxy

ft

DE

• this assumes that the facesheet is wavy and

its behavior is dominated by the bending

modulus

Wrinkling under shear

• since wrinkling is caused by the compressive load,

calculate the wrinkling load at 45o

• this means the necessary quantities must be rotated 45

degrees:

NxyNxy

Nxy

Nxy

45o x

y

x

y

oxzyz

xzyzzy

oxzyz

xzyzzx

forGG

GGG

forGG

GGG

452

sincos

452

cossin

22

22

__

__

(5.5.3.2.20)

Wrinkling under combined loads(1)

• use interaction curves

(1) Birman, V., Bert, C.W., “Wrinkling of Composite Facing Sandwich Panels Under Biaxial

Loading”, J Sandwich Structures and Materials, 6, 2004, pp. 217-237

Also: Ley, R.P., Lin, W., and Mbanefo, U., “Facesheet Wrinkling in Sandwich Structures”,

NASA/CR-1999-208994, January 1999

Wrinkling under combined loads –

Interaction curves

• biaxial compression 3/1

3

1

x

y

xwrx

N

N

NN

x is the core “major” direction

(with the higher shear stiffness

and strength)

• compression in x direction, tension in y direction

xwrx NN

as before; tension neither helps nor deteriorates performance

• compression and shear

xywrxys

xwrxc

sc

NNR

NNR

RR

/

/

12

Nx Nx

Ny

Ny

Nx Nx

Nxy

Nxy

Wrinkling under combined loads –

Interaction curves

• biaxial compression and shear

xywrxys

xwrxc

sc

NNR

NNR

RR

/

/

12

here Nxwr is wrinkling load in major core direction when biaxial loading acts alone!

• compression in x dir, tension in y dir, and shear

xywrxys

xwrxc

sc

NNR

NNR

RR

/

/

12

here Nxwr is wrinkling load in the compr. direction when compr. loading acts alone!

Shear crimping5.5.3.3

• this is a failure mode that is very similar to the anti-

symmetric wrinkling but with, essentially, zero

wavelength

ℓ 0

Shear crimping under compression

• if the wavelength tends to zero, the column buckling

or local buckling NEcrit that depend on the wavelength

go to infinity because

2

1

EcritN

• using eq (5.5.3.1.2), which is the basic equation for

sandwich buckling load, and setting NEcrit=∞,

1

Ecrit

cc

cc

crit

N

Gt

GtN

NEcrit∞

cccrit GtN

with Gc=Gxz or Gyz depending on

the direction of loading

(5.5.3.3.1)

Shear crimping under shear

yzxzcxycrim GGtN (5.5.3.3.2)

Dimpling or intracellular buckling

x

y

z

tc

s

cell size

5.5.3.4

• for sufficiently large cell size s, the facesheet may

buckle in between the cell walls=> dimpling


• a rigorous approach to determine the dimpling load would

require determination of the buckling load for composite

plates with non-rectangular shapes

– hexagonal for regular Nomex, HFT, Korex, etc. cores

– even more complex for flex-core

– or double flex-core


• instead, it can be shown by comparing to test results

that the following expression, derived from column

buckling considerations) is conservative:

2

3

dim

1

12

s

tEN

yxxy

ff

x

(5.5.3.4.1)

ss

• with s the cell size obtained as the diameter of the

circle shown below:

Other considerations for sandwich

structure

• rampdown

– frequently, sandwich attaching to adjacent parts

must be ramped down for better attachment and load

transfer

5.5.4

rampdown

Rampdown considerations

θ

Layup?

θ?

Rampdown considerations(1)

1. Kassapoglou, C., "Stress Determination and Core Failure Analysis in Sandwich Rampdown Structures

Under Bending Loads", Fracture of Composites, E. Armanios editor, TransTech Publications, Switzerland,

1996, pp 307-326

• eccentricity poses problems; sandwich bends

even under in-plane load

• large deflections for typical panel size

θ

monolithic

region

transition

regionfull-depth

region


θ

monolithic

region

transition

regionfull-depth

region

• Layup:

– full-depth is determined by panel requirements

(buckling, strength in the presence of damage, etc.)

– monolithic is determined by attachment requirements

(bearing strength, bonded joint analysis, etc.)

– transition is a smooth transition from monolithic to full

depth PROVIDED:


core machining at

plydrop locations?tc

1-2 core thicknesses10 x dropped height-half

core thicknessmore and stiffer material

must come up the ramp

to attempt to load both

facesheets evenly

• sufficient plies go up the ramp to transfer load evenly

Rampdown considerations• ramp angle θ

θ

– very hard to get load up the

ramp

– danger of crushing core from

the edge during cure

θ close to 90o

cure pressure

may crush

core θ

θ close to 0o

– can achieve load distribution 60/

40 among facesheets (or better)

– no crushing during cure (for

θ≈40-45 need stabilization)

– large transition region => low

bending stiffness

– handling and curing problems

with core sharp edge

core too thin to

handle and will move

during cure


• under certain assumptions(1) can show that the optimum

angle is ~18 degrees

• in practice, angles 20-30 are preferred; 45 degrees to a

lesser extent

1. Kassapoglou, C., "Stress Determination and Core Failure Analysis in Sandwich Rampdown Structures

Under Bending Loads", Fracture of Composites, E. Armanios editor, TransTech Publications, Switzerland,

1996, pp 307-326

θ

Alternatives to rampdown

“Pi” joints “F” joints

adhesive

adhesive

• if the joints are pre-cured, cannot use film adhesive;

must use paste adhesive=> issues with bondline control

• can also co-cure (no adhesive?) if the facesheets are at

least staged

Application 3 – Sandwich under

compression

tc=?

ribbon direction

1270 mm

1016 mm

121.45

N/mm

Basic mat’l

properties:

Ex=137.88 GPa

Ey=11.03 GPa

Gxy=4.826 GPa

νxy=0.29

tply=0.1524 mm

x

y

Layup : [45/-45/0/core/0/-45/45]

Candidate core materials

Material Ec (MPa) Gxz (MPa)

(Ribbon direction)

Gyz (MPa)

HRH-1/8-3.0 133.1 42.05 24.12

HRH-3/16-3.0 122.7 39.29 24.12

cell size (units of

inches)

density (units of

lb/ft3)

core A

core B

per

facesheet


compression

1. Determine the minimum core thickness needed for

each type of core material for the sandwich panel not

to fail

2. What is the minimum core thickness needed if the

core is misplaced and the ribbon direction rotated by

90 degrees? (sloppiness of manufacturing personnel)


compression

• from classical laminated-plate theory, for each

facesheet45/-45/0 0/-45/45

A11(N/mm) 34527.5 34527.5

A12(N/mm) 10927 10927

A16(N/mm) 0 0

A22(N/mm) 15069.25 15069.25

A26(N/mm) 0 0

A66(N/mm) 11662 11662

D11(Nmm) 713.1893 713.1893

D12(Nmm) 153.7698 153.7698

D16(Nmm) 112.9 112.9

D22(Nmm) 223.7678 223.7678

D26(Nmm) 112.9 112.9

D66(Nmm) 166.5275 166.5275

E1m(GPa) 1.02E+04 1.02E+04

vxy 0.725 0.725

vyx 0.317 0.317

Ef=

not negligible any

more; our results will

be “approximate”

Application 3 – Sandwich failure modes

2

2)(2)(2

fc

fijfijij

ttADD

• from eq. (5.5.1) the bending stiffnesses for the entire

sandwich are given by

(5.5.1)

• as the core thickness varies, the sandwich Dij terms

are

these are negligible again so

panel buckling is not affected

by disregarding them

tc (mm)--> 5.08 7.62 12.7 15.24 25.4 30.48 35.56 38.1

D11(Nmm) 530728.97 1127704 2989908 4255137 11543573 16524301 22396036 25666031

D12(Nmm) 167817.19 356743.1 946079.3 1346490 3653078 5229341 7087583 8122446

D16(Nmm) 225.8 225.8 225.8 225.8 225.8 225.8 225.8 225.8

D22(Nmm) 231457.4 492002.1 1304746 1856946 5037925 7211723 9774395 11201558

D26(Nmm) 225.8 225.8 225.8 225.8 225.8 225.8 225.8 225.8

D66(Nmm) 179110.17 380744.1 1009722 1437065 3898806 5581095 7564331 8668804


• for panel buckling use eq (5.5.3.1.2)

1

Ecrit

cc

cc

crit

N

Gt

GtN (5.5.3.1.2)

to substitute in eq. (5.5.3.1.3)

22

4

22

22

6612

4

11

2 )()()2(2

ma

ARDARmDDmDNEcrit

(5.5.3.1.3)

NEcrit(N/mm) 280.6621 596.4966 1581.712 2251.093 6107.102 8742.199 11848.69 13578.71

tc (mm)--> 5.08 7.62 12.7 15.24 25.4 30.48 35.56 38.1

core A Ncrit(N/mm) 121.25851 208.3761 399.0801 498.6265 908.668 1117.284 1327.109 1432.343

Core B Ncrit(N/mm) 116.61081 199.2769 379.1845 472.797 857.4491 1052.843 1249.261 1347.741

lower than but

almost equal to

applied load

solution for buckling is between these

two thicknesses

applied load = 121.45

N/mm


• for wrinkling, eq (5.5.3.2.18)


N/mm

• wrinkling load is independent of the core thickness;

both configurations (core A and core B) have wrinkling

strength higher than the applied load => any core

thickness will work

3/143.0 xzcffxwr GEEtN (5.5.3.2.18)

tc (mm)--> 5.08 7.62 12.7 15.24 25.4 30.48 35.56 38.1

core A Nxwr(N/mm) 282.85831 282.8583 282.8583 282.8583 282.8583 282.8583 282.8583 282.8583

Core B Nxwr(N/mm) 269.19049 269.1905 269.1905 269.1905 269.1905 269.1905 269.1905 269.1905

per facesheet!x 2 for entire panel


• the shear crimping load given by eq (5.5.3.3.1)

cccrit GtN (5.5.3.3.1)

is always higher than the buckling load given by eq

(5.5.3.1.2) so whichever core thickness works for

buckling will also work for crimping

2

3

dim

1

12

s

tEN

yxxy

ff

x

• for dimpling or intracellular buckling, the failure load,

given by eq. (5.5.3.4.1)

is independent of core thickness (x 2 for entire panel)

same for all

thicknesses applied load = 121.45

N/mm

for entire panel!

per facesheet!

core A Nxdim(N/mm) 3396.0192

Core B Nxdim(N/mm) 1509.3419

0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25 30 35 40

core thickness (mm)

Lo

ad

(N

/mm

)

.

Buckling core ABuckling core B

wrinkling core A

wrinkling core B

applied load

Application 3 – Sandwich failure modes• summarizing all results,

see enlargement next page


• core thickness = 5.1 mm for core A and 5.3 mm for core B

0

100

200

5 6 7 8 9 10

core thickness (mm)

Lo

ad

(N

/mm

)

.

Buckling core ABuckling core B

applied load

5.1 mm ~5.3 mm

Application 3 – Some thoughts

• strictly speaking, for such low core thicknesses, one

should check if the core thickness selected satisfies the

requirement implied by the wrinkling eq. used (that less

than full core depth is effective in deformation); but

because we are using the design eq with 0.43 factor

instead of 0.91, there is (usually) no need to do that

Application 3 – Part 2(mislocating the core)

• in terms of core contribution to panel performance, the

worst that can happen is to rotate the core by 90o during

manufacturing so the weakest direction is aligned with

the applied load

• in this case the panel buckling and wrinkling loads are

reduced significantly

•applying eqs. (5.5.3.1.2) and (5.5.3.2.18) but using Gyz

instead of Gxz that was used before, gives the plot in the

next page

Application 3 – Part 2(mislocating the core)


N/mm

0

200

400

600

800

1000

5 10 15 20

core thickness (mm)

Lo

ad

(N

/mm

)

.

~6.75 mm

panel buckling

wrinkling core A

applied load

Symmetric wrinkling - TU Delft OCW · 2016-02-02 · the failure mode switches from antisymmetric...

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